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Real Analysis Topology and Sigma-Algebra

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1). Prove that any sigma-algebra, which contains a finite number of members is also a topology. ( The Q in another words : to show that there exist a sequence of disjoint members of a sigma algebra which contains infinite no. of members).

2). Does there exist an infinite sigma-algebra which has only countably many members? (Of course justify, examples, anything needed to prove any claims made in the solution.)

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Solution Summary

Sigma-algebras are investigated. The solution is detailed and well presented.

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1. Proof:
We check the definition of sigma-algebra of topology. Suppose F is a sigma-algebra defined on the set X. We want to show that F is also a ...

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